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Optimal convergence rates for Tikhonov regularization in Besov scales
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D. A. Lorenz
Published/Copyright:
February 4, 2009
Abstract
In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales.
Received: 2008-07-25
Published Online: 2009-02-04
Published in Print: 2009-February
© de Gruyter 2009
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Keywords for this article
Tikhonov regularization;
Besov space;
scales of Banach spaces;
convergence rate
Articles in the same Issue
- Minisymposium — Recent progress in regularization theory
- Recent results on the quasi-optimality principle
- An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space
- Regularization in Banach spaces — convergence rates by approximative source conditions
- On a parameter identification problem in linear elasticity
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
